MathDB
Problems
Contests
International Contests
APMO
2005 APMO
1
1
Part of
2005 APMO
Problems
(1)
rational and irrational
Source: APMO 2005 Problem 1
3/23/2005
Prove that for every irrational real number
a
a
a
, there are irrational real numbers
b
b
b
and
b
′
b'
b
′
so that
a
+
b
a+b
a
+
b
and
a
b
′
ab'
a
b
′
are both rational while
a
b
ab
ab
and
a
+
b
′
a+b'
a
+
b
′
are both irrational.